A police van moving on a highway with a speed of `30 km h^(-1)` Fires a bullet at a thief's car speeding away in a same direction with a speed of `192 km h^(-1)`. If the muzzle speed of the buller is `150 m s^(-1)`, with what speed does the bullet hit thief's car? .
.

Options

A. `95 m s^(-1)`
B. `105 m s^(-1)`
C. `115 m s^(-1)`
D. `125 m s^(-1)`

Answer

B

Explanation

Speed of police van w.r.t ground `therefore v_PG = 30 km h^(-1)`
Speed of thief's car w.r.t ground `therefore v_PG = 192 km h^(-1)`
Speed of bullet w.r.t police van
`v_BP = 150 m s^(-1) = 150 xx 18/5 km h^(-1) = 540 km h^(-1)`
Speed with which the bullet will hit the thief's car will be
`v_BT = v_BG + v_GT = v_BP + v_PG + v_GT`
= `540 km h^(-1) + 30 km h^(-1) - 192 km h^(-1)`
(since `v_GT = -v_TG)`
`= 378 km h^(-1) = 378 xx 5/18 m s^(-1)= 105 m s^(-1)`